Convergence Analysis And EFG Of A Tresca Frictional Contact Problem For Elastic Material

Element-free Galerkin method(EFG)is a meshfree method based on weak form.This method has the advantage of high numerical accuracy and stability and it's the most popular meshfree method.In this paper,EFG is introduced in detail and it's applied to solve boundary value problems of the second class of elliptic variational inequalities,and the static and quasistatic Tresca frictional contact problems for elastic materials.The main contents in this paper are as follows:1.In chapter 2,it introduces EFG method for the second class of elliptic variational inequalities and presents the numerical algorithm for EFG.It proves the convergence theorems for EFG method.To verify the efficiency of EFG method,numerical examples are realized.It demonstrates the effect of different domains to numerical results,Moreover,different boundary conditions and different weight functions are also disscussed.2.It presents the static Tresca frictional contact problems for elastic materials in chapter 3.The physical background and variational formulation of static Tresca frictional contact problem is given in detail.The error estimation and convergence analysis of EFG are provided.Numerical examples demonstrate the efficiency of EFG method.Moreover,it extends the results to the problem subject to the Coulomb friction condition.3.The quasistatic Tresca frictional contact problems for elastic materials is discussed in chapter 4.Using the MLS approximation and time difference method discretize the spatial and time derivatives respectively,it constructed the EFG discrete scheme for the quasistatic Tresca frictional contact problems for elastic materials.Finally,the convergence and error estimation of EFG scheme is obtained?...